Well logs are obtained by lowering logging tools down the well and recording a series of data at different depths. Logging tools can be categorized in terms of their operating tool physics. They include resistivity tools, nuclear tools, acoustics tools, Nuclear Magnetic Resonance (NMR) tools, etc. Also, logging tools can be grouped based on the scenario in which the tool operates, e.g., Wireline Logging (WL) tools and Logging While Drilling (LWD) tools. WL tools are lowered into a well by attaching them to a wireline. Wireline Logging is the traditional way for collecting well logs. LWD is a more recent development in which logging tools are mounted on drill collars and logging is performed while drilling is going on. After well logs are collected, data processing techniques are often applied to facilitate data interpretation and well log analysis. Various data processing techniques exist for resistivity, acoustic, nuclear and NMR logs. Resolution enhancement of well logs has always been of interest to the oil and gas industry because such techniques improve accuracy in thinly bedded reservoir evaluation.
Resolution enhancement has been approached in different ways by professionals in the oil and gas industry. One is based on linear deconvolution and other is a nonlinear approach. Linear deconvolution utilizes deconvolution filters to deconvolve tool response to a target response function with a well-defined shape and resolution. For resistivity log processing, the popular choice for such target functions are Gaussian functions with 1 ft., 2 ft., or 4 ft. resolutions. A modern logging tool commonly has multiple depths of investigations as in the case of WL array induction and LWD propagation tools. The measurement at different depths of investigation usually produces different vertical resolutions. Linear deconvolution not only enhances vertical resolutions but also matches resolutions of all measurements at different depths of investigations at a preselected resolution. For example, if a 1 ft. target function is used in linear deconvolution, then measurement from all depths of investigations will be processed to have the same resolution at 1 ft. Such a linear deconvolution technique is described in U.S. Pat. No. 5,429,335 for processing LWD propagation logs. However, linear deconvolution is limited by the operating tool physics. When the tool response is very nonlinear, linear deconvolution will produce unacceptable artifacts. For induction tools, linearity worsens when the resistivity contrast in formation beds increases. High-contrast formations are not uncommon in well logging. For example, a shale formation can have resistivity at around 1 Ohm-m, while an anhydrite formation nearby can have resistivity at thousands of Ohm-m. Linearity also worsens when the operating frequency is higher. Thus, linear deconvolution has been recognized as insufficient in many scenarios.
To ameliorate the artifacts caused by the nonlinearity of the tool response, nonlinear resolution enhancement techniques have been developed. Nonlinear techniques are typically more robust than linear techniques, especially for logs acquired in high-contrast formations. One such method is described in U.S. Pat. No. 5,967,906, which recites a nonlinear enhancement similar to a Van Cittert iterative deconvolution technique that utilizes nonlinear modeling of the tool response rather than the response functions as in linear deconvolution techniques. The enhancement is performed on a square log and the enhanced square log is subsequently smoothed to produce the reduced resolution. A disadvantage of this enhancement technique is the amount of correction required on the original log can be very large for each iteration, which may lead to instabilities in a Van Cittert nonlinear enhancement process. Therefore, subsequent smoothing is always necessary for this technique as the last step in processing. In addition, although the technique mentions how to provide matched resolutions among different tool spacings, it fails to describe how to match resolutions at a preselected value, e.g. a fixed 2 ft. resolution.